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• To: seaint(--nospam--at)seaint.org
• Subject: Re: square tubing loads
• From: Charley Hamilton <chamilto(--nospam--at)uci.edu>
• Date: Thu, 29 May 2003 15:14:26 -0700

```Stephen -

```
I am an aspiring engineer, first year undergraduate,
```> designing a table using 2" x 2" square tubing as legs.

*woof*  I assume that the 2" dimension is cosmetic, since
it's almost certainly not going to be necessary for a table.

> I would like to know how to determine the lightest carbon
> steel material (thinnest wall) capable of supporting loads of
> up to 300 lbs., 400 lbs...

Remember that, despite the planned design loads, furniture
One of my fondest memories from undergraduate structural analysis
is the day we designed a desk chair:

Professor:  "What if the person leans back on one leg like this?
What loads do you have to consider in that case?"

[Chair (and professor) topple backwards onto the floor]

Think about what people might end up doing with the table:
changing lightbulbs, storing large piles of textbooks, dragging
it back and forth across the floor (although using 2" HSS
will tend to discourage this), etc.  Thinking about these
to provide.  Also, don't forget self-weight if that table is to
be fabricated from structural steel.

The required wall thickness is driven by four potential
"failure" modes:

- axial compressive yielding   (unlikely for a table)
- axial shortening under load  (probably negligible for 2" sq HSS)
- wall buckling  (likely negligible unless you can find much thinner
walls than I see in the HSS specification)
- member buckling  (only really a concern for long members given the
kinds of loads you describe later in the email)

```
Shall I refer to charts? Should I
```> know a formula for calculating the load limit using material
> thickness as the variable? where might I find formulas for different
> types of material, for example round tubing, angle iron, square bar?

I would be prone to simply calc it out using
first principles.

Depending on the course work you have already
completed, I would say that an elementary mechanics of
materials course should allow you to compute the axial
stresses in the column members and bending stresses in
the table-top members (assuming the table acts like a frame),
which will effectively give the the required moment of
inertia for the section.  Remember to model the frame as
having a pinned base (the bottoms of table legs are
generally unlikely to develop substantial moment resistance).

Also, mechanics of materials should have covered simple
Euler buckling, which you can check to ensure that you
have an adequate moment of inertia (again, highly unlikely
to be a problem in this case) to prevent member buckling.

For wall buckling, however, you probably need to do
a little digging to get an understanding of how to
do the calculations.  Purely on a hunch, I'd say you
could go as low at 1/16" wall thickness and still be
relatively safe against wall buckling for 2" HSS.

As far as tables go, the American Institute of Steel
Construction (AISC) has the Manual of Steel Construction
(MSC), which is intended to facilitate either
allowable-stress or ultimate-strength design
(depending on your edition) of steel structures.
However, you need to understand the basic principles which
the MSC employs before you can effectively use it.
Theoretically you could use the MSC for this purpose, but
it seems gross overkill for designing a table.

Of course, an HSS 2.5 x 2.5 x 1/8 has an axial capacity
(phi*Pn) of just under 6 kips for a 16 foot unbraced span
according to LRFD 3rd Edn. MSC Table 4-6, and that's already
under 4 plf of self-weight, so your troubles may be over,
assuming the slenderness checks work out.  Check out
the LRFD specifications for HSS (hollow structural
AISC's website.  This will give you some understanding of
what you're getting into if you run a code analysis of
the HSS table legs.

Similar information is available for angles, round HSS,
pipe, etc.  If you're looking for *very* thin wall tubes,
you may ned to check AISI specifications for material
properties and run first-principle calcs for the axial
deformation, yielding, and global/local buckling issues
based on specific geometric data from metal suppliers.

> Thank you in advance. It is to my great advantage to be
> allowed to listen in to the conversations of you all

I was in your shoes not *that* long ago, and it's in
many ways to our advantage to have young engineers
such as yourself "eavesdrop" on the conversations here.
The reality of practice generally provides a different
viewpoint on engineering than one would obtain in the
classroom, which often enhances one's understanding of
engineering.

Best of luck and have fun designing the table.

Charley Hamilton

--
Charles Hamilton, PhD EIT               Faculty Fellow
Department of Civil and                 Phone: 949.824.3752
Environmental Engineering           FAX:   949.824.2117
University of California, Irvine        Email: chamilto(--nospam--at)uci.edu

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